two months in india, route suggestion?

I have planned to travel in india from JAN.10 to MAR.20, after a short stay in singapore, . and will fly to Thiruvananthapuram the first step. and then north to delhi, and east to kolkata, from there leave to thailand. after a study on maps, here is what i'm thinking about:

this has includ. most the places recommended. but as Udaipur seems not approachable by train, and amritsar is a bit outside...any comments and suggestions here for the route considering the time and local festivals? and I would like to travel around by train as much as possible when it's convenient...